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Printable Law of Cosines SSS Worksheet | Grades 10-12 Math
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This Law of Cosines worksheet teaches students to find a missing angle when all three sides of a triangle are known. Learners rearrange the formula to isolate cosine, apply inverse cosine, and judge whether an angle is acute or obtuse before calculating, so their answers make sense.
At a Glance
- Grade: 10–12 · Subject: Math
- Standard:
HSG-SRT.D.11— Use the Law of Cosines to find unknown angles when three sides are known- Skill Focus: Finding a missing angle from three sides (SSS)
- Format: 3 pages · 24 problems · Answer key included · PDF
- Best For: Law of Cosines practice after instruction
- Time: 25–35 minutes
What's Inside
The 3-page worksheet has three parts, and each part opens with a worked example. Part A covers rearranging the formula to solve for cos A, cos B, and cos C. Part B has 12 triangle problems with side lengths in mixed units. Part C has 4 estimate-then-solve problems. A 3-page answer key lists every angle.
Skill Progression
- Guided practice: Part A, rearranging the Law of Cosines with a worked example and a given starting formula.
- Supported practice: Part B, 12 problems with a worked example and reminders to keep full calculator precision, use degree mode, and round to the nearest tenth.
- Independent practice: Part C, 4 problems where students decide acute or obtuse, solve, and check.
The flow follows gradual release: I Do, We Do, You Do.
Standards Alignment
HSG-SRT.D.11 — Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles. This worksheet targets the Law of Cosines with three known sides. The standard code can be copied directly into lesson plans, IEP goals, or district curriculum mapping tools.
How to Use It
- During or right after direct instruction: Assign Parts A and B as guided classwork once the formula has been modeled.
- Before a quiz: Use Part C as a review set to build estimating habits.
Formative tip: while students work Part C, ask them to explain why the longest side's square decides acute or obtuse. Students who skip the estimate often miss calculator errors. Expect 25–35 minutes.
Who It's For
Students in Grades 10–12 taking Geometry, Algebra II, or Precalculus. Students who need more support can start with the worked examples and Part A. Students ready for more can write a sentence justifying each estimate in Part B. Pair it with a Law of Cosines anchor chart or a direct-instruction lesson.
The Law of Cosines SSS Worksheet for Grades 10–12 Math supports standard HSG-SRT.D.11, which asks students to apply the Law of Cosines to find unknown measurements in non-right triangles. Across 3 pages and 24 problems, students rearrange the formula to cos C = (a² + b² − c²) / (2ab), use inverse cosine in degree mode, and round to the nearest tenth of a degree. They also estimate whether the largest angle is acute or obtuse by comparing squared side lengths, then check the calculated angle against that prediction. The sequence follows the gradual release model described by Fisher & Frey (2014): a worked example, supported practice, then independent work. A three-page answer key shows final angles for every problem, so teachers can scan for common errors such as degree-mode mistakes, sign slips, and misplaced squares during review.
